Slimani, AliKhemis, Rabah2024-04-152024-04-152023http://dspace.univ-skikda.dz:4000/handle/123456789/940In this thesis, we use a system of nonlinear PDEs, or the conventional d-dimensional parabolicparabolic equation, to explain the Keller-Segel chemotaxis model. These PDEs include a convectiondiffusion equation for the cell density and a reaction-diffusion equation for the chemoattractant concentration. The Keller-Segel chemotaxis model explains how the density of a cell population and the concentration of an attractant change over time. This thesis uses a variety of approaches and strategies to investigate the parabolic Keller-Segel equations. In the first, we talk about the biological and mathematical modeling of the phenomenon of chemical entrapment, and we create a non-linear fractional stochastic Keller-Segel model, where we demonstrate the existence and uniqueness and regularity properties of the mild solution to the investigated time- and space-fractional problem and the required results under specific presumptions. We also studied a stochastic chemotaxis Keller-Segel model perturbed with a Gaussian process, where we proved the local and global existence of solutions in time for a nonlinear stochastic Keller-Segel model with zero Dirichlet boundary conditions, and we also studied the phenomenon of the Keller-Segel model coupled with Boussinesq equations. The primary goals of this work are to investigate the global existence and uniqueness of a weak solution of the problem using the Galerkin method. Finally, we studied the numerical solution of one-dimensional Keller-Segel equations via the new homotopy perturbation method.enThesis